Effect of viscous dissipation on natural convection heat and mass transfer from vertical cone in a non-Newtonian fluid saturated non-Darcy porous medium

In this paper we investigate the influence of viscous dissipation and Soret effect on natural convection heat and mass transfer from vertical cone in a non-Darcy porous media saturated with non-Newtonian fluid. The surface of the cone and the ambient medium are maintained at constant but different levels of temperature and concentration. The Ostwald-de Waele power law model is used to characterize the non-Newtonian fluid behavior. The governing equations are non-dimensionalized into non-similar form and then solved numerically by local non-similarity method. The effect of non-Darcy parameter, viscous dissipation parameter, Soret parameter, buoyancy ratio, Lewis number and the power-law index parameter on the temperature and concentration field as well as on the heat and mass transfer coefficients is analyzed.     

Effects of variable viscosity on non-Darcy MHD free convection along a non-isothermal vertical surface in a thermally stratified porous medium

An analysis is performed for non-Darcy free convection flow of an electrically conducting fluid over an impermeable vertical plate embedded in a thermally stratified, fluid saturated porous medium for the case of power-law surface temperature. The present work examines the effects of non-Darcian flow phenomena, variable viscosity, Hartmann–Darcy number and thermal stratification on free convective transport and demonstrates the variation in heat transfer prediction based on three different flow models. The wall effect on porosity variation is approximated by an exponential function. The effects of thermal dispersion and variable stagnant thermal conductivity are taken into consideration in the energy equation. The resulting non-similar system of equations is solved using a finite difference method. Results are presented for velocity, temperature profiles and local Nusselt number for representative values of different controlling parameters.     

Analytical approach to heat and mass transfer in MHD free convection from amoving permeable vertical surface

An analytical study is performed on heat and mass transfer in MHD‐free convection from a moving permeable vertical surface and the results are compared with previous works on this phenomenon to test the validity. The coupled equations of boundary layer are transformed from their non‐linear form to ordinary form using similarity transformation and then are solved by a newly developed method, homotopy analysis method. Having different base functions, homotopy analysis method provides us with great freedom in choosing the solution of a nonlinear problem. Solving the boundry layer equations, the effects of different parameters such as magnetic field strength parameter (M), Prandtl number (Pr), Schmidt number (Sc), buoyancy ratio and suction/blowing parameter (f_w) on velocity, temperature, and concentration profiles are taken into consideration. Obtained results show that increment of magnetic field strength parameter (M) leads to decrease in velocity profile. Copyright © 2011 John Wiley & Sons, Ltd.     

Influence of radiation on MHD free convection from a vertical flat plate embedded in porous media with thermophoretic deposition of particles

Magneto-hydrodynamics and thermal radiation effects on heat and mass transfer in steady laminar boundary layer flow of a Newtonian, viscous fluid over a vertical flat plate embedded in a fluid saturated porous media in the presence of the thermophoresis particle deposition effect is studied in this paper. The governing equations are transformed by special transformations. Brownian motion of particles and thermophoretic transport are considered in the flow equations. The magnetic field is considered to be applied. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The resulting similarity equations are solved numerically by the fourth-order Runge–Kutta method with shooting technique. Many results are obtained and representative set is displayed graphically to illustrate the influence of the various parameters on the wall thermophoretic deposition velocity, concentration, temperature and velocity profiles.     

Network simulation method applied to radiation and viscous dissipation effects on MHD unsteady free convection over vertical porous plate

The effects of thermal radiation and viscous dissipation on magneto-hydrodynamic (MHD) unsteady free-convection flow over a semi-infinite vertical porous plate are analysed. The fluid considered is non-gray (absorption coefficient dependent on wave length). The Network Simulation Method is used to solve the boundary-layer equations based on the finite-difference formulation; only discretization of the spatial co-ordinates is necessary, while time remains as a real continuous variable. This method provides a solution for both transient and steady-state problems at the same time, and programming does not require manipulation of the sophisticated mathematical software that is inherent in other numerical methods. The velocity, temperature, local skin-friction and local Nusselt number are studied for different parameters, including the radiation parameter, Eckert number, magnetic number and suction (or injection).     

Numerical study of viscous dissipation effect on free convection heat and mass transfer of MHD non-Newtonian fluid flow through a porous medium

The problem of free convection heat with mass transfer for MHD non-Newtonian Eyring–Powell flow through a porous medium, over an infinite vertical plate is studied. Taking into account the effects of both viscous dissipation and heat source. The temperature and concentration are of periodic variation. The governing non-linear partial differential equations of this phenomenon are transformed into non-linear algebraic system utilizing finite difference method. Numerical results for the velocity, temperature and concentration distributions as well as the skin friction, heat and mass transfer are obtained and reported in tabular form and graphically for different values of physical parameters of the problem. Also, the stability condition is studied.     

Lie group analysis of natural convection heat and mass transfer in an inclined surface with chemical reaction

In this paper we examine the convective flow, heat and mass transfer of an incompressible viscous fluid past a semi-infinite inclined surface with first-order homogeneous chemical reaction by Lie group analysis. The governing partial differential equations are reduced to a system of ordinary differential equations using scaling symmetries. Numerical solutions of the resulting ordinary differential equations are obtained using the fourth-order Runge–Kutta method. From the numerical results, it is observed that the thickness of the momentum boundary layer increases with increasing the chemical reaction parameter and the Schmidt number. The thicknesses of the thermal and concentration boundary layers are decreased with increasing the chemical reaction parameter and the Schmidt number.     

Peristatcally induced MHD slip flow in a porous medium due to a surface acoustic wavy wall

The influences of Hall current and slip condition on the MHD flow induced by sinusoidal peristaltic wavy wall in two dimensional viscous fluid through a porous medium for moderately large Reynolds number is considered on the basis of boundary layer theory in the case where the thickness of the boundary layer is larger than the amplitude of the wavy wall. Solutions are obtained in terms of a series expansion with respect to small amplitude by a regular perturbation method. Graphs of velocity components, both for the outer and inner flows for various values of the Reynolds number, slip parameter, Hall and magnetic parameters are drawn. The inner and outer solutions are matched by the matching process. An interesting application of the present results to mechanical engineering may be the possibility of the fluid transportation without an external pressure.     

MHD non-Darcy mixed convective diffusion of species over a stretching sheet embedded in a porous medium with non-uniform heat source/sink, variable viscosity and Soret effect

The effects of temperature dependent viscosity and non-uniform heat source/sink on non-Darcy MHD mixed convection boundary layer flow over a vertical stretching sheet embedded in a fluid-saturated porous media is studied in this paper. Boundary layer equations are transformed into ordinary differential equations using self-similarity transformation which are then solved numerically using fifth-order Runge-Kutta-Fehlberg method with shooting technique for various values of the governing parameters. The effects of variable viscosity, porosity, electric field parameter, non-uniform heat source/sink parameters, Soret number and Schmidt number on concentration profiles are analyzed and discussed. Favorable comparisons with previously published work on various special cases of the problem are obtained. Numerical results for variation of the local Sherwood number with buoyancy parameter, Schmidt number, and Soret number are reported graphically to show some interesting aspects of the physical parameters.     

Influence of variable heat flux on natural convection along a corrugated wall in porous media

In this work the coupled non-linear partial differential equations, governing the free convection from a wavy vertical wall under a power law heat flux condition, are solved numerically. For both Darcy and Forchheimer extended non-Darcy models, a wavy to flat surface transformation is applied and the governing equations are reduced to boundary layer equations. A finite difference scheme based on the Keller Box approach has been used in conjunction with a block tri-diagonal solver for obtaining the solution. Detailed simulations are carried out to investigate the effect of varying parameters such as power law heat flux exponent m, wavelength–amplitude ratio a and the transformed Grashof number Gr′. Both surface undulations and inertial forces increase the temperature of the vertical surface while increasing m reduces it. The wavy pattern observed in surface temperature plots, become more prominent with increasing m or a but reduces as Gr′ increases.     

Natural convection flow from a horizontal circular cylinder with uniform heat flux in presence of heat generation

Natural convection boundary layer laminar flow from a horizontal circular cylinder with uniform heat flux in presence of heat generation has been investigated. The governing boundary layer equations are transformed into a non-dimensional form and the resulting non-linear systems of partial differential equations, which are solved numerically by two distinct methods namely: (i) implicit finite difference method together with the Keller-box scheme and (ii) perturbation solution technique. The results of the surface shear stress in terms of local skin-friction and the rate of heat transfer in terms of local Nusselt number, velocity distribution, velocity vectors, temperature distribution as well as streamlines, isotherms and isolines of pressure are shown by graphically for a selection of parameter set consisting of heat generation parameter.     

The influence of heat and mass transfer on MHD peristaltic flow through a porous space with compliant walls

The present study investigates the effects of heat and mass transfer on peristaltic transport in a porous space with compliant walls. The fluid is electrically conducting in the presence of a uniform magnetic field. Analytic solution is carried out under long-wavelength and low-Reynolds number approximations. The expressions for stream function, temperature, concentration and heat transfer coefficient are obtained. Numerical results are graphically discussed for various values of physical parameters of interest.     

Effects of radiation and variable viscosity on unsteady MHD flow of a rotating fluid from stretching surface in porous medium

This work is focused on the study of unsteady magnetohydrodynamics boundary-layer flow and heat transfer for a viscous laminar incompressible electrically conducting and rotating fluid due to a stretching surface embedded in a saturated porous medium with a temperature-dependent viscosity in the presence of a magnetic field and thermal radiation effects. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. With appropriate transformations, the unsteady MHD boundary layer equations are reduced to local nonsimilarity equations. Numerical solutions of these equations are obtained by using the Runge–Kutta integration scheme as well as the local nonsimilarity method with second order truncation. Comparisons with previously published work have been conducted and the results are found to be in excellent agreement. A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity in primary and secondary flows as well as the local skin-friction coefficients and the local Nusselt number are illustrated graphically to show interesting features of Darcy number, viscosity-variation, magnetic field, rotation of the fluid, and conduction radiation parameters.     

Non-Darcy free convection flow over a horizontal cylinder in a saturated porous medium with variable viscosity,thermal conductivity and mass diffusivity

In this paper, the effects of variable viscosity and thermal conductivity on coupled heat and mass transfer by free convection about a permeable horizontal cylinder embedded in porous media using Ergun mode are studied. The fluid viscosity and thermal conductivity and are assumed to vary as a linear function of temperature while the mass diffusion is assumed to vary as linear function of concentration. The surface of the horizontal cylinder is maintained at a uniform wall temperature and a uniform wall concentration. The transformed governing equations are obtained and solved by using the implicit finite difference method. Numerical results for dimensionless temperature and concentration profiles as well as Nusselt and Sherwood numbers are presented for various values of parameters namely, Ergun number, transpiration parameter, Rayleigh and Lewis numbers and buoyancy ratio parameter.     

Lie group analysis of unsteady MHD three dimensional by natural convection from an inclined stretching surface saturated porous medium

Lie group method is investigated for solving the problem of heat transfer in an unsteady, three-dimensional, laminar, boundary-layer flow of a viscous, incompressible and electrically conducting fluid over inclined permeable surface embedded in porous medium in the presence of a uniform magnetic field and heat generation/absorption effects. A uniform magnetic field is applied in the y-direction and a generalized flow model is presented to include the effects of the macroscopic viscous term and the microscopic permeability of porous medium. The infinitesimal generators accepted by the equations are calculated and the extension of the Lie algebra for the problem is also presented. The restrictions imposed by the boundary conditions on the generators are calculated. The investigation of the three-independent-variable partial differential equations is converted into a two-independent-variable system by using one subgroup of the general group. The resulting equations are solved numerically with the perturbation solution for various times. Velocity, temperature and pressure profiles, surface shear stresses, and wall-heat transfer rate are discussed for various values of Prandtl number, Hartmann number, Darcy number, heat generation/absorption coefficient, and surface mass-transfer coefficient.     

Peristaltic transport of a Newtonian fluid in a vertical asymmetric channel with heat transfer and porous medium

The problem of peristaltic flow of a Newtonian fluid with heat transfer in a vertical asymmetric channel through porous medium is studied under long-wavelength and low-Reynolds number assumptions. The flow is examined in a wave frame of reference moving with the velocity of the wave. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. The analytical solution has been obtained in the form of temperature from which an axial velocity, stream function and pressure gradient have been derived. The effects of permeability parameter, Grashof number, heat source/sink parameter, phase difference, varying channel width and wave amplitudes on the pressure gradient, velocity, pressure drop, the phenomenon of trapping and shear stress are discussed numerically and explained graphically.     

Effects of Hall current and heat transfer on rotating flow of a second grade fluid through a porous medium

The effects of Hall current and heat transfer on the rotating flow of a second grade fluid past a porous plate with variable suction are examined. The medium considered is porous and suction and external flow velocities vary periodically. The plate is assumed to be at a higher temperature than the fluid. The influences of the Hall parameter and porosity of the medium have been seen and discussed on the velocity and temperature profiles. Moreover, these influences have also been seen on the drag and lateral stress. Finally, the obtained solutions are also compared with the previous studies in the literature and found quite agreement.     

Combined effect of magnetic field and heat absorption on unsteady free convection and heat transfer flow in a micropolar fluid past a semi-infinite moving plate with viscous dissipation using element free Galerkin method

The fully developed electrically conducting micropolar fluid flow and heat transfer along a semi-infinite vertical porous moving plate is studied including the effect of viscous heating and in the presence of a magnetic field applied transversely to the direction of the flow. The Darcy-Brinkman-Forchheimer model which includes the effects of boundary and inertia forces is employed. The differential equations governing the problem have been transformed by a similarity transformation into a system of non-dimensional differential equations which are solved numerically by element free Galerkin method. Profiles for velocity, microrotation and temperature are presented for a wide range of plate velocity, viscosity ratio, Darcy number, Forchhimer number, magnetic field parameter, heat absorption parameter and the micropolar parameter. The skin friction and Nusselt numbers at the plates are also shown graphically. The present problem has significant applications in chemical engineering, materials processing, solar porous wafer absorber systems and metallurgy.     

Buoyancy and chemical reaction effects on MHD mixed convection heat and mass transfer in a porous medium with thermal radiation and Ohmic heating

The combined effect of mixed convection with thermal radiation and chemical reaction on MHD flow of viscous and electrically conducting fluid past a vertical permeable surface embedded in a porous medium is analyzed. The heat equation includes the terms involving the radiative heat flux, Ohmic dissipation, viscous dissipation and the internal absorption whereas the mass transfer equation includes the effects of chemically reactive species of first-order. The non-linear coupled differential equations are solved analytically by perturbation technique. The results obtained show that the velocity, temperature and concentration fields are appreciably influenced by the presence of chemical reaction, thermal stratification and magnetic field. It is observed that the effect of thermal radiation and magnetic field is to decrease the velocity, temperature and concentration profiles in the boundary layer. There is also considerable effect of magnetic field and chemical reaction on skin-friction coefficient and Nusselt number.